The following is an explanation from the Met' Office as to what triggers a warning and why sometimes one isn't triggered.
Follows no warning been issued on 28-29th June 2017 when parts of Cumbria had very heavy rain.

The National Severe Weather Warning Service (NSWWS) became an impact based warning service in March 2011. This means that, rather than issuing warnings based upon strict meteorological thresholds, warnings are now issued based upon an assessment of the impact that the weather may cause. The NSWWS is a UK wide service, and gives a general overview of potentially impactful weather over a fairly large area, so any weather details in the warning (rainfall amounts, wind speeds, snow accumulations, low temperatures etc) are giving an indication of the weather over a large area rather than at specific locations within the warning area.

The NSWWS also has different audiences, with differing levels of engagement/interest in weather and its impacts. Responder organisations such as the Police, Fire Service, Ambulance, NHS, local authorities and the Environment Agency use the warnings as part of their planning and preparation to enable an effective response to severe weather and its impacts. Amongst the public, there are those that take a great interest in the weather, but there are also many who have far less of an interest and there is a challenge in trying to get the impact message across to those who are likely to be affected by severe weather to enable them to alter travel plans, protect their properties etc. This is why warnings can be issued or updated during the evening or overnight i.e. in order to catch the news bulletins before people go to bed or to ensure that it makes the early morning bulletins before people go out for the day.

A number of factors are taken into account when considering whether to issue a warning, what areas to include and at what level the warning should be issued. For rainfall warnings, Met Office forecasters link with Environment Agency (EA) hydrologists through the Flood Forecasting Centre to assess the flood risk. This includes the potential for river, surface water and coastal flooding, and the impact assessment also involves input from local EA staff on the current conditions in their area. Other factors that are also considered to varying degrees depending upon the particular circumstances at the time are;
• Time of year – is this forecast weather unusual for the time of year? Will there be lots of visitors to an area in summer – out on the hills, camping etc – who aren’t used to local weather?
• Time of day/day of week – less impact is likely if the severe weather occurs overnight at the weekend than if it occurs during a rush hour during the week.
• Regional climatology – is the weather unusual for this part of the country?
• Change of weather type – after a long dry spell could heavy rain be a surprise to many? After a fairly mild spell in winter, will a spell of snow and ice catch people out?
• Affecting rural or urban areas – rural areas tend to be less populated, but a closed road in a rural area can lead to a very long diversion and a greater impact on local communities. Urban areas are likely to be less affected by the closure of a single, local road, but impacts on motorways and major commuter routes can cause widespread impacts on an area. The problems are different but just as significant in each area.

So what does all this mean for your 54mm? Well, in very basic terms there are 3 possible scenarios assuming that the event is within the forecast parameters (which it was):
• The ground is bone dry and so although the watercourses are capable of taking the additional volume, the rain takes a time to soak in and therefore runs off quickly as surface water causing potential damage or a threat to life. A warning would be issued for this.
• The ground is at or near saturation point and/or the rivers are nearing their capacity. In this situation even a little extra volume could cause damage or a threat to life and a warning would be issued.
• The ground is receptive to moisture, the aquifers are well below their maximum and the rivers are well within their normal range. This scenario would not warrant a warning as there would be no threat to life or property. This is the situation that occurred this week.

From a personal point of view I can appreciate that 54mm is a sizeable daily amount of rain. However, having been out inspecting this week I can say from firsthand experience that it was ‘uncomfortable’ but I didn’t come across any roads closed due to rain or any other form of flood damage. For the same reason that the Police don’t respond to every RTC on ‘blues-n-twos’, the Met Office don’t issue a warning for every sizeable rainfall event. Conversely, given the right (or should that be wrong) circumstances, a warning could be issued for an ‘unremarkable’ 20-25mm.

I hope that has answered your concerns about the lack of any Sever Weather Warning. The short answer is that one was not required because no impact was anticipated.
Best regards